Surveys in Differential Geometry
Volume 11 (2006)
Perelman’s Stability Theorem
Pages: 103 – 136
We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with $\curv$ $\ge k$ Gromov-Hausdorff converging to a compact Alexandrov $X$, $X_i$ is homeomorphic to $X$ for all large $i$.